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A general multivariate threshold GARCH model with dynamic conditional correlations

  • Fabio Trojani

    ()

  • Francesco Audrino

We propose a new multivariate DCC-GARCH model that extends existing approaches by admitting multivariate thresholds in conditional volatilities and conditional correlations. Model estimation is numerically feasible in large dimensions and positive semi-definiteness of conditional covariance matrices is naturally ensured by the pure model structure. Conditional thresholds in volatilities and correlations are estimated from the data, together with all other model parameters. We study the performance of our approach in some Monte Carlo simulations, where it is shown that the model is able to fit correctly a GARCH-type dynamics and a complex threshold structure in conditional volatilities and correlations of simulated data. In a real data application to international equity markets, we observe estimated conditional volatilities that are strongly influenced by GARCH-type and multivariate threshold effects. Conditional correlations, instead, are determined by simple threshold structures where no GARCH-type effect could be identified.

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Paper provided by Department of Economics, University of St. Gallen in its series University of St. Gallen Department of Economics working paper series 2005 with number 2005-04.

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Length: 41 pages
Date of creation: Jan 2005
Date of revision:
Handle: RePEc:usg:dp2005:2005-04
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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  2. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
  3. Hamao, Yasushi & Masulis, Ronald W & Ng, Victor, 1990. "Correlations in Price Changes and Volatility across International Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 281-307.
  4. Ledoit, Olivier & Santa-Clara, Pedro & Wolf, Michael, 1999. "Flexible Multivariate GARCH Modeling With an Application to International Stock Markets," University of California at Los Angeles, Anderson Graduate School of Management qt93s6p8gb, Anderson Graduate School of Management, UCLA.
  5. Kim, S.W. & Rogers, J.H., 1993. "International Stock Price Spillovers and Market Liberalization: Evidence from Korea, Japan, and the United States," Papers 4-93-7, Pennsylvania State - Department of Economics.
  6. Adrian Pagan, 1985. "Two Stage and Related Estimators and Their Applications," Cowles Foundation Discussion Papers 741, Cowles Foundation for Research in Economics, Yale University.
  7. Audrino, Francesco, 2006. "Tree-Structured Multiple Regimes in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 338-353, July.
  8. Bae, Kee-Hong & Andrew Karolyi, G., 1994. "Good news, bad news and international spillovers of stock return volatility between Japan and the U.S," Pacific-Basin Finance Journal, Elsevier, vol. 2(4), pages 405-438, December.
  9. Koutmos, Gregory & Booth, G Geoffrey, 1995. "Asymmetric volatility transmission in international stock markets," Journal of International Money and Finance, Elsevier, vol. 14(6), pages 747-762, December.
  10. Mervyn A. King & Sushil Wadhwani, 1989. "Transmission of Volatility Between Stock Markets," NBER Working Papers 2910, National Bureau of Economic Research, Inc.
  11. Robert F. Engle & Takatoshi Ito & Wen-Ling Lin, 1988. "Meteor Showers or Heat Waves? Heteroskedastic Intra-Daily Volatility in the Foreign Exchange Market," NBER Working Papers 2609, National Bureau of Economic Research, Inc.
  12. Becker, Kent G. & Finnerty, Joseph E. & Friedman, Joseph, 1995. "Economic news and equity market linkages between the U.S. and U.K," Journal of Banking & Finance, Elsevier, vol. 19(7), pages 1191-1210, October.
  13. Fulvio Corsi & Francesco Audrino, 2007. "Realized Correlation Tick-by-Tick," University of St. Gallen Department of Economics working paper series 2007 2007-02, Department of Economics, University of St. Gallen.
  14. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  15. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  16. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  17. Fabio Trojani & Francesco Audrino, 2006. "Estimating and predicting multivariate volatility thresholds in global stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 345-369.
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